Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Algorithmic aspects of vertex elimination on directed graphs.
Algorithmic aspects of vertex elimination on directed graphs.
Organization of clustered files for consecutive retrieval
ACM Transactions on Database Systems (TODS)
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
Dominating the complements of bounded tolerance graphs and the complements of trapezoid graphs
Discrete Applied Mathematics
Hamiltonicity of regular graphs and blocks of consecutive ones in symmetric matrices
Discrete Applied Mathematics
On the hardness of minimizing space for all-shortest-path interval routing schemes
Theoretical Computer Science
Recognizing bipartite tolerance graphs in linear time
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Four lessons in versatility or how query languages adapt to the web
Semantic techniques for the web
MPQ-trees for the Orthogonal Packing Problem
Journal of Mathematical Modelling and Algorithms
The black-and-white coloring problem on distance-hereditary graphs and strongly chordal graphs
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
A convexity upper bound for the number of maximal bicliques of a bipartite graph
Discrete Applied Mathematics
| Hi-index | 0.00 |
A matrix of zeroes and ones is said to have the consecutive ones property if there is a permutation of its rows such that the ones in each column appear consecutively. This paper develops a data structure which may be used to test a matrix for the consecutive ones property, and produce the desired permutation of the rows, in linear time. One application of the consecutive ones property is in recognizing interval graphs. A graph is an interval graph if there exists a 1-1 correspondence between its vertices and a set of intervals on the real line such that two vertices are adjacent if and only if the corresponding intervals have a nonempty intersection. Fulkerson and Gross have characterized interval graphs as those for which the clique versus vertex incidence matrix has the consecutive ones property. In testing this particular matrix for the consecutive ones property we may process the columns in a special order to simplify the algorithm. This yields the interval graph recognition algorithm which is presented in section 2; section 3 indicates how this algorithm may be extended to the general consecutive ones problem.